Bancroft's, an independent school in east London, was first hit by tragedy last summer when former pupil Grace O'Malley-Kumar died as she tried to protect her friend Barnaby Webber as he was fatally stabbed.
The boy who died in Hainault on Tuesday, who has not yet been identified by police, also attended the school.
His mother works at Holy Family Catholic School, which published a statement on its website addressed to parents and carers that said: “It is with great sadness that I share with you the news of the death of the child of one of our staff members.
"Mrs Anjorin’s son was taken from this life suddenly this morning on his way to school. Please keep Mrs Anjorin, her husband and their other children in your prayers."
Speaking on "Good Morning Britain" on Wednesday, O'Malley-Kumar's father Dr Sanjoy Kumar said the boy’s loved ones will be distraught.
He said: "It's absolutely appalling. You can't even imagine what the parents are going through. This is just the most difficult thing for any parents to endure.
"It's something that we've endured now for many months, and I can tell you that the distraught that the family are feeling is only felt by a few like us who have lost children in these absolutely appalling circumstances."
A female police officer who suffered "horrifically serious" arm injuries was one of four people who were hurt in the horror attack.
Metropolitan Police Commissioner Mark Rowley said she is facing "a long journey of recovery" after nearly losing her hand.
He told LBC: "The surgeon spent many, many hours basically putting her arm back together."
A male officer also suffered serious hand injuries and is recovering in hospital.
Rowley went on: "People say officers run towards danger.
"What you've actually seen on some of the videos that are around social media and on news sites...you actually see what that really looks like.
"You've got officers running towards someone who's waving a sword."
Prime Minister Rishi Sunak paid tribute to those affected by the attack at the beginning of Prime Minister’s Questions on Wednesday.
He said: "Such violence has no place on our streets. It is absolutely heartbreaking that a teenage boy has died and I can’t imagine what his family are going through, and we send them our heartfelt condolences and offer our very best wishes to all those injured.
"I would just like to reiterate my thanks to the police and other emergency first responders for embodying the highest standards of public service under such awful circumstances."
The horror unfolded in Hainault on Tuesday morning when a man armed with a sword went on the rampage, killing the teenage boy and injuring two other members of the public as well as the two police officers.
Neighbours said the attacker first spoke to a woman, asking her to confirm his location, before she saw the weapon and fled. She tried to warn the teenage victim, said to be a Nigerian boy, but it was too late.
Speaking about the victim, Rowley said: "The first thing you have to say is for the parents involved, who’ve lost their 14-year-old, that is just horrific, and it's everyone's worst nightmare.
"I'm sure we’re all thinking about them."
Terrified residents hid as the swordsman climbed over garden fences, before police managed to Taser and arrest him.
The 36-year-old suspect remains in hospital after being injured when he crashed his van into a house.
Chief Superintendent Stuart Bell, of the Metropolitan Police, said he did not believe it was a targeted attack, and it is not believed to be terror-related.
Amid speculation about previous police contact with the suspect, Metropolitan Police Assistant Commissioner Louisa Rolfe said on Tuesday that “no trace of a prior incident” involving him had been found, but that the force will continue to make checks.
Dramatic footage obtained by the PA news agency captured the suspect being cornered and tasered by officers on a residential driveway.
The video shows officers shouting at the suspect, saying "Don't move, don't fucking move" after he is brought to the ground by three separate Taser discharges.
The words "Suspect contained" are eventually heard as a female officer pulls the sword away from the attacker.
A Buckingham Palace spokesman said King Charles III's "thoughts and prayers are with all those affected" by the "horrific" stabbings, adding: "In particular, the family of the young victim who has lost his life."